Emily is twice as old as Charlotte. Four years ago, the product of their ages was 30. Use a quadratic equation to find Charlotte's present age.

First I said E (Emily) = 2C (Charlotte)

Then . . .

(E-4)*(C-4)=30

EC-4E-4C+16=30

EC-4E-4C=14

EC-4E-4C-14=0

Next I substituted in [E=2C]

(2C*C)-(2C*4)-4C-14=0

2C^2-8C-4C-14=0

2C^2-12C-14=0

Then I factorised . . .

2*(C^2-6C-7)=0

2*(C-7)*(C+1)=0

So Charlotte's present age must be 7.

To check it . . .

E=2*7=14

(E-4)*(C-4)=30

(14-4)*(7-4)=30

10*3=30

I thought this might interest at least one person.

zacismyname
May 3, 2015

#2**+5 **

Nice

I didn't think of doing it like that. The more direct route for sure.

zacismyname
May 3, 2015

#1**+5 **

Very nice, zacismyname !!! ....you're correct.....this is a good one !!!

We could also do it with one varable from the start :

Let Charlotte's age be x and Emily's age be 2x

So we have

(2x - 4)(x - 4) = 30

2x^2 - 12x + 16 = 30

2x^2 - 12x - 14 = 0

x^2 - 6x - 7 = 0

(x - 7) (x + 1) = 0 so x = 7 or x = -1 .....reject - 1 .....

So.....x = 7 = Charlotte's age and 2(7) = 14 = Emily's age

Just as you found !!!!

CPhill
May 3, 2015

#2**+5 **

Best Answer

Nice

I didn't think of doing it like that. The more direct route for sure.

zacismyname
May 3, 2015